Finite Group DatabasebetaFinite Group Databasebeta← (C3×AGL(1,ℤ/9))⋊C9 #13090654
Order 1458.
230 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624560 | C2 | semidirect |
| 3. C3×D9⋊C9 | C3 | semidirect |
| 5. C3×C9×D9 | C3 | semidirect |
| 7. C3×C9⋊C9 | C2×C3 | semidirect |
| 10. C3×C92 | C2×C3 | semidirect |
| 17. C3×AGL(1,ℤ/9) | C9 | semidirect |
| 32. C3×3−1+2 | C2×C9 | semidirect |
| 98. C3×C9 | AGL(1,ℤ/9) | semidirect |
| 115. D9 | C32⋊C9 | semidirect |
| 144. C9 | C2×C32⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624560 | 2 |
| C32×AGL(1,ℤ/9) | 3 |
| C3×D9⋊C9 | 3 |
| D3×C32⋊C9 | 3 |
| C3×C9×D9 | 3 |